#14060: Improve minimal_quadratic_twist()
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Reporter: cremona | Owner: cremona
Type: defect | Status: new
Priority: major | Milestone: sage-6.1
Component: elliptic curves | Resolution:
Keywords: pari precision | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Changes (by cremona):
* cc: wuthrich (added)
Comment:
I see two possibilities here: either rename this function
{{{minimal_twist()}}} and return (as it does now) a curve which may be a
sextic or quartic twist when j=0 or j=1728; or keep this name and be
more restrictive for those j-invariants so that the returned curve
literally is a quadratic twist. A third possibility is to have both named
functions, doing the same thing unless j=0 or j=1728.
I am CC-ing Chris W since the only place where this function is used
(according to {{{search_src()}}}) is in {{{sha_tate.py}}}, line 540, and
whatever we do must be compatible with what is needed there!
Of course this is in addition to adding one line to return self of
{{{self.conductor().is_squarefree()}}}.
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Ticket URL: <http://trac.sagemath.org/ticket/14060#comment:3>
Sage <http://www.sagemath.org>
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